The interaction between nodes is modeled as an undirected network \(\mathcal {G}=(\mathcal {V},\mathcal {E}, W)\) , where \(\mathcal {V}=\lbrace 1,2,\cdots ,n\rbrace \)  is the set of nodes, \(\mathcal {E}\subseteq \mathcal {V}\times \mathcal {V}\)  is the set of edges, and edge \((i,j)\in \mathcal {E}\)  if and only if nodes \(i\)  and \(j\)  can directly exchange compressed messages with each other. \(\mathcal {G}\)  is called connected if there exists a path between any pair of nodes. We denote the set of nodes that directly communicate with node \(i\)  as the neighbors of \(i\) , i.e., \(\mathcal {N}_i=\lbrace j|(j,i)\in \mathcal {E}\rbrace \cup \lbrace i\rbrace \) . \(W\in \mathbb {R}^{n\times n}\)  is an adjacency matrix of \(\mathcal {G}\) , i.e., \([W]_{ij}=0\)  if \((i,j)\notin \mathcal {E}\) . It captures the interactions between neighboring nodes, e.g., \(WX\)  can be evaluated via local communications, where \(X=[\mathbf {x}_1,\cdots ,\mathbf {x}_n]^\mathsf {T}\)  and \(\mathbf {x}_i\)  denotes the local copy of node \(i\) . We make the following standard assumption [1]}, [2]}:
